What is Apparent depth: Definition and 24 Discussions

In physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.
For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equal to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the indices of refraction (n2 / n1) of the two media.

















{\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}

Optical prisms and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light, and thus the angle of the refraction also varies correspondingly. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.

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  1. L

    Apparent depth of an object underwater

    I would know how to solve this problem if the person had been standing pratically above of the object underwater by using Snell's law and the approximation ##\sin(\theta)\approx\tan(\theta)## fopr ##\theta## small, but in this case I don't see how to find the angles ##\theta_1## and ##\theta_2##...
  2. jaumzaum

    B Apparent Depth - What remains constant?

    Hello! Just now I began to question myself about something I learned many years ago. When we are outside of a pool and see a coin in the floor of the pool (underwater) we think that the coin has an apparent depth that is smaller than the real depth. To calculate this we extrapolate the light...
  3. R

    Viewing Particle P in a Cylindrical Vessel - 40 cm Height Needed

    I1. Homework Statement A cylindrical vessel whose diameter and height both are equal to 30 cm is placed on a horizontal surface and a small particle p is placed in it at a distance of 5 cm from the centre. An eye is placed at a position such that the edge of the bottom is in the plane of...
  4. esha

    Apparent depth when two or more refracting surfaces are present

    I know the concept of apparent depth as such: It is the depth at which an object is seen when viewed from a different medium. But i want to know what happens when two refracting surfaces are kept one after the other. In the given diagram let the object be placed at the bottom of the vessel...
  5. Biker

    Thin lens approximation and Apparent depth

    So we are studying optics in school this semster, Very interseting topic I say but I just have a couple of question I want to ask. In concave and convex mirror, we study spherical ones where F = R/2. I was able to prove this and that it is only an approximation when ## R >> h_o ## or ## h_0##...
  6. RabbitWho

    Finding apparent depth real depth and refractive index

    Homework Statement refractive index = 1.33 (water) real depth = 10m Homework Equations refractive index = real depth divided by apparent depth The Attempt at a Solution I'm going to call apparent depth X 1.33 = 10/x So I multiply 10/x by 10 so that i have x and 1.33 x 10 is 13.3... that's...
  7. A

    B Understanding the Apparent Depth Equation: Explained and Simplified

    Hi, can someone please explain to me where this equation derives from and how it works? d'=d(n2/n1) where d'=the apparent depth of the object, d=the actual depth, n1= the index of refraction of the medium in which the refracted light travels, and n1= the index of refraction of the medium in...
  8. Clack_Attack

    I Apparent depth conceptual question

    You know the proofs for finding the apparent depth of a swimming pool, or object submerged in one? Well, it always assumes the object is directly above the original object. Does anyone know where the assumption comes from? (see below)
  9. S

    Apparent depth equation proving

    Homework Statement a fish at a depth d underwater.Takes the index of refraction of water as 4/3 show that when the fish is viewed at an angle of refraction θ , the apparent depth z of the fish is z = (3d cosθ )/ √ (7 + 9 cos2 θ) Homework Equations snell's law n1 x sin θ1 = n2 x sin θ2 The...
  10. Suraj M

    Calculating RI of Oil w.r.t Air with Apparent Depth of Liquid

    Homework Statement This is how my teacher dictated the question... ---A layer of oil 3 cm thick is floating on a layer of coloured water 5 cm thick, the RI of the coloured water with respect to the oil is ##\frac{5}{3}##. The apparent depth of the liquid is ##\frac{36}{7} cm##. What is the RI...
  11. S

    Apparent Depth of Light Bulb above Water and Mirror

    Homework Statement Hey, so there is a light bulb above a tank of water which has a mirror at the bottom. I am trying to find the apparent depth of the image of the light produced by the mirror. Finding the apparent depth of the mirror is easy, but I am confused on what to consider the object...
  12. S

    Real and apparent depth

    Homework Statement Hi. I need help with homework. the correct answers have been provided in the question. one doesn't match with mine and the other does. I don't understand how the one answer can be correct when its dependent on my incorrect answer. A transparent cube of 15cm edge contains a...
  13. A

    Calculating Apparent Depth of Print Beneath Flint Glass Plate

    Homework Statement A flint glass plate 3.5 cm thick is placed over a newspaper. How far beneath the top surface of the plate would the print appear to be if you were looking almost vertically downward through the plate? Homework Equations N=1.66 for flint glass Apparent = d/n The...
  14. R

    Refraction (aperture, apparent depth)

    Homework Statement 1: A decrease in the aperture of a lens changes the (A)Size of the image (B)Intensity of the image (C)Portion of the image (D) All of these 2: A vessel is filled with two different liquids which do not mix. One liquid is 40cm deep and has n=1.6 and the other is 30cm deep...
  15. E

    Find Apparent depth due to a non-homogenous liquid

    THE ACTUAL PROBLEM: A vessel of depth H is filled with a non-homogenous liquid whose refractive index varies with y as u=(2 -(y/H)), where y is measured from bottom of the vessel. Find the apparent depth as seen by an observer from above? (Paraxial approximation is allowed) RELEVANT...
  16. P

    Real and apparent depth

    Hi all, I have this problem : A coin is dipped to the bottom of a water filled container made of an opaque material. Observed from the water surface, the depth of the coin appears to be 2 meters. Find the real depth ( R.I. of water = 1.33 ) Since angles are not given, how do I apply...
  17. R

    Apparent depth and snells law

    Homework Statement A fish is 80 cm below the surface of a pond. What is the apparent depth (in cm) when viewed from a position almost directly above the fish? (For water, n = 1.33.) Homework Equations Snell's law: n_1 sin \theta_1 = n_2 sin \theta_2 The Attempt at a Solution So...
  18. K

    Apparent depth with multiple indices of refraction

    Homework Statement A penny is located at the bottom of a barrel of water 1m deep. There is a 20cm thick layer of oil on top of the water. To an observer at normal incidence, what is the apparent depth of the penny. n for water is 1.33, for oil it is 1.5 Homework Equations Snell's law...
  19. S

    Apparent depth of water

    Any help how to approach this problem. The depth of pond is 10m. What is the apparent depth for a person looking normally to the water surface? ( Refractive index )water =4/3.
  20. R

    Apparent depth involving benzene on water

    Homework Statement In a vessel, a layer of benzene (n=1.50) 6 cm deep floats on water (n=1.33) 4 cm deep. Determine the apparent distance of the bottom of the vessel below the upper surface of the benzene when viewed vertically through air. Ans 7 cm Homework Equations Snell's law n sin...
  21. A

    Calculating Apparent Depth: Air vs Water

    Homework Statement Instead of calculating apparent depth (for example, a penny in a glass of water appears to be closer to the surface than it actually is), instead of finding the angle of refraction and using snell's law, can I use the following: Apparent Depth = Actual Depth x (n air / n...
  22. L

    Apparent Depth Problem

    Homework Statement A beaker has a height of 40.0 cm. The lower half of the beaker is filled with water (n = 1.333), and the upper half is filled with oil (n = 1.48). To a person looking down into the beaker from above, what is the apparent depth of the bottom? Homework Equations...
  23. C

    Actual Depth and Apparent Depth

    Okay, I need a bit of a jump start with this question, I know how to find the Apparent depth normally, but I've never done actual depth and I can't really figure it out (*stupid*) 11. Frederika is sitting in her fishing boat observing a rainbow trout swimming below the surface of the water...
  24. P

    Physics - optics - apparent depth

    My physics textbook has a diagram that illustrates Apparent Depth... but I can't understand it. Specifically, why does the image appear where it is (at apparent depth)? I understand that as the light from the object moves from water to air, refraction occurs... but I'm thinking, shouldn't...